Theorems · Theorem · logic and foundations

PrimrecRel.listFilter

∀ {α : Type u_1} {β : Type u_2} {R : α → β → Prop} [inst : Primcodable α] [inst_1 : Primcodable β],
  PrimrecRel R → ∀ [inst_2 : DecidableRel R], Primrec₂ fun L b => List.filter (fun a => decide (R a b)) L

If R a b is decidable, then given L : List α and b : β, it is primitive recursive to filter L for elements a with R a b

Defined in

Mathlib.Computability.Primrec.List

Cited by

2 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PrimcodablePrimcodableDecidableRel